Chapter 8.2, Problem 2P

For each of the following differential equations, separate variables and find a solution containing one arbitrary constant. Then find the value of the constant to give a particular solution satisfying the given boundary condition. Computer plot a slope field and some of the solution curves.

$x\sqrt{1-y^2}dx+y\sqrt{1-x^2}dy=0,$ $y=\frac{1}{2}$ when $x=\frac{1}{2}.$